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Strategies  and  Interventions  to  Support  Students  with  Mathematics  Disabilities  

 Brittany  L.  Hott,  PhD  Laura  Isbell,  PhD  Texas  A&M  University-­‐  Commerce    Teresa  Oettinger  Montani,  EdD  Fairleigh  Dickinson  University  (December  2014) In  the  absence  of  intensive  instruction  and  intervention,  students  with  mathematics  difficulties  and  disabilities  lag  significantly  behind  their  peers  (Jitendra  et  al.,  2013;  Sayeski  &  Paulsen,  2010).  Conservative  estimates  indicate  that  25%  to  35%  of  students  struggle  with  mathematics  knowledge  and  application  skills  in  general  education  classrooms,  indicating  the  presence  of  mathematics  difficulty  (Mazzocco,  2007).  Additionally,  5%  to  8%  of  all  school-­‐age  students  have  such  significant  deficits  that  impact  their  ability  to  solve  computation  and/or  application  problems  that  they  require  special  education  services  (Geary,  2004).  This  InfoSheet  provides  an  overview  of  strategies  and  resources  to  support  students  with,  or  at-­‐risk  for,  mathematics  learning  disabilities.  

Common  Core  Mathematics  Standards  

With  the  current  emphasis  on  the  Common  Core  State  Standards  (CCSS;  National  Governors  Association  Center  for  Best  Practices  [NGA  Center],  2010,  2014),  it  is  

essential  that  students  with  math  difficulties  and  disabilities  be  prepared  to  meet  with  success  on  these  newly  articulated  grade  level  expectations  in  mathematics.  Special  education  teachers  and  general  education  teachers  need  to  have  strategies  to  help  students  who  struggle  with  mathematics  to  gain  access  to  the  general  education  curriculum  and  to  meet  with  success  in  all  areas  of  math  including  math  literacy  and  conceptual  knowledge  (Gargiulo  &  Metcalf,  2013;  Powell,  Fuchs,  &  Fuchs,  2013).  

Although  the  CCSS  do  not  provide  a  curriculum,  they  do  specify  the  topics  within  standards  that  should  be  addressed  by  grade  level.  CCSS  included  two  major  components:  Standards  for  Mathematics  Practice  and  Standards  for  Mathematics  Content.  These  standards  indicate  that  students  should  be  able  to  (1)  make  sense  of  problems  and  persevere  in  solving  them,  (2)  reason  abstractly  and  quantitatively,  (3)  construct  viable  arguments  and  critique  the  reasoning  of  others,  (4)  model  with  mathematics,  (5)  use  appropriate  tools  strategically,  (6)  attend  to  precision,  (7)  look  for  and  make  use  of  

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structure,  and  (8)  look  for  and  express  regularity  in  repeated  practices.  During  the  elementary  years,  focus  is  placed  on  mathematics  fundamentals  with  the  goal  of  moving  from  counting  skills  to  multiplying  and  dividing  fractions.  By  middle  school,  students  are  expected  to  understand  geometry,  ratios  and  proportions,  and  pre-­‐algebra  skills.  During  high  school,  the  focus  is  on  more  advanced  algebra,  functions,  modeling,  advanced  geometry,  statistics,  and  probability  content.  For  a  complete  listing  of  grade  level  standards  download  the  complete  set  of  grade  specific  standards  (www.corestandards.org/the-­‐standards/mathematics).  

The  Early  Learning  in  Mathematics  program  (Davis  &  Jungjohann,  2009)  is  an  example  of  a  core  mathematics  program  that  embodies  the  current  thinking  on  effective  instruction  in  math  (Doabler  et  al.,  2012).  Both  systematic  and  explicit  instruction  and  detailed  coverage  of  significant  areas  of  content  in  mathematics  are  addressed  in  this  program.  The  successful  elements  of  explicit  and  systematic  instruction  incorporated  in  this  program  that  can  also  be  utilized  in  other  core  mathematics  instruction  include  the  following:  

1. Specific  and  clear  teacher  models  2. Examples  that  are  sequenced  in  level  

of  difficulty  3. Scaffolding  4. Consistent  feedback  5. Frequent  opportunity  for  cumulative  

review  (NCEERA,  2009)  Fuchs  and  Fuchs  (2008)  identified  seven  

principals  of  effective  practice  for  primary  

students  with  math  disabilities.  In  their  article,  the  authors  stated  that  third  grade  is  a  time  when  mathematical  disabilities  tend  to  be  identified,  and  used  the  seven  interventions  to  illustrate  the  principles.  The  seven  principles  include  (1)  instructional  explicitness,  (2)  instructional  design  to  minimize  the  learning  challenge,  (3)  provide  strong  conceptual  knowledge  for  procedures  taught,  (4)  drill  and  practice,  (5)  cumulative  review,  (6)  motivation  to  help  students  regulate  their  attention  and  behavior  and  to  work  hard,  and  (7)  on-­‐going  progress  monitoring.   Strategies  for  Teaching  Problem  Solving  Skills    Strategy  training  has  been  helpful  to  students  with  LD  when  learning  mathematical  concepts  and  procedures.  The  following  are  a  few  examples  of  strategies  that  are  useful  to  teachers  when  instructing  students  with  LD  in  problem  solving.   RIDE  (Mercer,  Mercer,  &  Pullen,  2011)  RIDE  is  a  strategy  used  to  assist  students  with  solving  word  problems.  Students  who  experience  difficulty  with  abstract  reasoning,  attention,  memory,  and/or  visual  spatial  skills  may  benefit  from  the  strategy.  Ensure  that  steps  are  taught  through  demonstration  and  plenty  of  opportunities  for  practice  are  provided  before  asking  students  to  independently  use  the  strategy.  Visually  display  the  strategy  on  a  chart  or  class  website  as  a  reminder.  

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R-- Remember the problem correctly

I-- Identify the relevant information

D-- Determine the operations and unit for expressing the answer E-- Enter the correct numbers, calculate and check the answer

FAST  DRAW  (Mercer  &  Miller,  1992)  Like  RIDE,  FAST  DRAW  is  another  strategy  used  to  solve  word  problems.  Teach  each  step  in  the  sequence  allowing  sufficient  time  for  guided  practice  prior  to  asking  students  

to  independently  implement  the  strategy.  Create  a  visual  display  and  post  in  the  classroom  or  student  notebooks  to  assist  students.  

F— Find what you’re solving for. A— Ask yourself, “What are the parts of the problem?” S— Set up the numbers. T— Tie down the sign.

D — Discover the sign. R — Read the problem. A — Answer, or draw and check. W— Write the answer.

TINS  Strategy  (Owen,  2003)  The  TINS  strategy  allows  students  to  use  different  steps  to  analyze  and  solve  word  problems.  

T—Thought Think about what you need to do to solve this problem and circle the key words.

I— Information Circle and write the information needed to solve this problem; draw a picture; cross out unneeded information.

N— Number Sentence Write a number sentence to represent the problem. S-- Solution Sentence Write a solution sentence that explains your answer.

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Strategies  to  Support  Vocabulary  Development  

Strategies  that  can  help  students  improve  their  mathematic  vocabulary  include  (a)  pre-­‐teach  vocabulary,  (b)  mnemonic  techniques,  and  (c)  key  word  approaches.  These  strategies  are  only  a  few  strategies  available  to  help  enhance  students’  mathematics  vocabulary  comprehension.   Pre-­‐teach  Vocabulary  

• Use  representations,  both  pictorial  and  concrete,  to  emphasize  the  meaning  of  math  vocabulary  (Sliva,  2004).  

• Pretest  students’  knowledge  of  glossary  terms  in  their  math  textbook  and  teach  vocabulary  that  is  unknown  or  incorrect.  

Mnemonic  Techniques  • Teach  mnemonic  techniques  to  help  

remember  word  meanings.  • Use  mnemonic  instruction  to  help  

students  improve  their  memory  of  new  information  (The  Access  Center,  2006).  

Key  Word  Approach  • Use  the  keyword  approach  (e.g.,  

visualize  a  visor  as  the  keyword  for    

• divisor;  visualize  quotation  marks  as  the  keyword  for  quotient  (Mastropieri  &  Scruggs,  2002).  

Strategies  to  Assist  with  Teaching    

Algebraic  Concepts    

Algebra  is  introduced  in  elementary  school  as  students  learn  algebraic  reasoning  involving  patterns,  symbolism,  and  representations.  Students  experience  difficulty  with  algebra  for  various  reasons  including  difficulty  understanding  the  vocabulary  required  for  algebraic  reasoning,  difficulties  with  problem  solving,  and  difficulties  understanding  patterns  and  functions  necessary  for  algebraic  reasoning.  Possible  strategies  to  assist  with  teaching  algebraic  concepts  include,  but  are  not  limited  to,  (a)  teaching  key  vocabulary  needed  for  algebra,  (b)  providing  models  for  identifying  and  extending  patterns,  (c)  modeling  “think  aloud”  procedures  for  students  to  serve  as  examples  for  solving  equations  and  word  problems,  (d)  incorporating  technology  usage  (e.g.,  graphing  calculators)  (Bryant,  2008),  and  (e)  implementing  Star  Strategy  described  below  (Gagnon  &  Maccini,  2001).  

S— Search the word problem.

T— Translate the words into an equation in picture form A— Answer the problem R— Review the problem.

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CRA  and  CSA  Instructional  Methods   Maccini  and  Gagnon  (2005)  stated  that  the  STAR  strategy  incorporates  the  concrete-­‐Semiconcrete-­‐Abstract  (CSA)  instructional  sequence,  which  gradually  advances  to  abstract  ideas  using  the  following  progression:  (a)  concrete  stage,  (b)  semiconcrete  stage,  and  (c)  abstract  stage.  By  using  the  CSA  framework  teachers  can  incorporate  effective  teaching  components  to  teach  students  effectively  and  efficiently.  Students  progressively  move  through  each  stage  to  achieve  mastery  in  a  mathematic  concept.  

Using  multiple  representations,  beginning  with  the  concrete  level  and  moving  to  the  abstract  level,  is  an  effective  technique  in  helping  struggling  learners  solve  calculation  problems.  The  Concrete-­‐Representational-­‐Abstract  (CRA)  teaching  sequence  has  been  found  to  help  students  with  LD  learn  procedures  and  concepts  (Flores,  Hinton,  &  Strozier,  2014).  During  the  concrete  stage  students  are  in  the  “doing”  stage,  during  the  representational  stage  students  are  in  the  “seeing”  stage,  and  during  the  abstract  phase  students  are  in  the  “applying”  stage.  Students  move  through  the  phases  fluidly.

C— Concrete: students use three-dimensional objects to represent math problems R— Representational: students use pictures to represent math problems A— Abstract: students represent the problem using numerical symbols

C— Concrete: students use three-dimensional objects to represent math problems

S— Semiconcrete: students use two-

dimensional representation to draw pictures of the math problem

A— Abstract: students represent the problem using numerical symbols

Strategies  to  Assist  with  the  Use  of  

Metacognitive  Skills   Metacognition  refers  to  individuals’  awareness  of  how  they  think  and  plan  activities.  Metacognition  also  involves  strategizing,  monitoring  success  and  effort,  and  knowing  when  to  change  directions  or  to  try  a  different  approach  to  problem  solving.  Many  students  with  learning  difficulties  benefit  from  the  use  of  metacognitive  skills  to  help  them  focus  on  what  they  are  doing  and  to  plan  for  how  to  employ  strategies  as  needed  and  change  directions  when  appropriate  (Mevarech  &  Amrany,  2008).    A  few  examples  of  how  to  incorporate  metacognitive  strategies  include:  

• Demonstrating  “think-­‐alouds”  so  students  become  aware  of  how  one  talks  oneself  through  a  learning  task.  

• Demonstrating  the  use  of  graphic  organizers,  schematics,  and  visual  imagery.  

• Explicit,  direct  instruction  accompanied  by  modeling  of  self-­‐monitoring,  self-­‐talk,  and  self-­‐checks.  

Mathematics  Advisory  Panels  and  Their  

Reports   Developing  foundational  mathematics  skills  at  the  elementary  level  is  essential.  Maintaining  basic  skills  acquired  during  the  elementary  years  is  essential  as  students  move  toward  more  advanced  computational,  place  value,  and  fractional  concepts.  As  

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students  move  from  elementary  to  secondary  mathematics,  it  is  important  that  students  maintain  skills  mastered  and  that  teachers  continue  to  scaffold  instruction  and  provide  supports  to  ensure  that  foundational  skills  

are  addressed  while  affording  access  to  more  advanced  mathematics  concepts.  Below  are  links  to  various  advisory  panel  recommendations  for  effectively  teaching  mathematics.  

Panel Link National Commission on Mathematics and Science Teaching for the 21st Century—Before It’s Too Late

http://www.ptec.org/items/detail.cfm?ID=4059

National Research Council—Adding It Up: Helping Children Learn Mathematics

http://www.nap.edu/catalog.php?record_id=9822

RAND Mathematics Study Panel—Mathematical Proficiency for All Students

http://www.rand.org/pubs/monograph_reports/MR1643/index.html

Foundations for Success: The Final Report of the National Mathematics Advisory Panel

http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

The Access Center’s Math Problem Solving for Primary Elementary Students with Disabilities

http://www.k8accesscenter.org/training_resources/mathprimaryproblemsolving.asp

The Access Center’s Math Problem Solving for Upper Elementary Students with Disabilities

http://www.k8accesscenter.org/training_resources/MathPrblSlving_upperelem.asp

Resources  

There  are  numerous  website  and  resources  available  to  assist  with  mathematics  

instruction.    Following  are  suggested  websites  with  a  summary  of  resources  for  teaching  a  variety  of  mathematics  concepts  across  levels.  

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Website Resource www.cast.org http://www.factmonster.com/math/flashcards.html www.aplusmath.com/flashcards www.flash-cardmachine.com www.academicskillbuilders.com www.sunburst.com www.intellitools.com www.tomsnyder.com www.illuminations.nctm.org www.internet4classrooms.com http://ncisla.wceruw.org/teachers/index.html

• expand learning opportunities through universal design

• increase math fluency with web-based flashcards

• enhance fluency through the use

of web-based flashcards

• enhance fluency with the use of web-based flashcards

• support math and vocabulary

fluency (Brownell, Smith, Crockett, Griffin, 2012)

• research based achievement

solutions; standards based products prescriptive web based instruction K-5, digital classroom

• technology for preK – 8

classrooms, free downloads available.

• software for fluency, word

problems, graphing, etc.

• activities, lessons, standards web links for math education; preK-12.

• Common Core State Standards

internet sites for teaching mathematics in culturally responsive ways

• resources related to supporting

understanding of science and math

References   The  Access  Center.  (2006).  Using  mnemonic  

instruction  to  teach  math.  Retrieved  from  http://www.k8accesscenter.org  

Brownell,  M.  T.,  Smith,  S.  J.,  Crockett,  J.  B.,  &  Griffin,  C.  C.  (2012).  Inclusive  instruction:  Evidence  based  practices  for  teaching  students  with  disabilities.  New  York,  NY:  The  Guilford  Press.  

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Bryant,  D.  P.  (2008).  Teaching  mathematics.  In  D.  P.  Bryant,  D.  D.  Smith,  &  B.  R.  Bryant  (Eds.),  Teaching  students  with  special  needs  in  inclusive  classrooms.  Boston,  MA:  Allyn  &  Bacon.  

Davis,  K.,  &  Jungjohann,  K.  (2009).  Early  learning  in  mathematics:  Level  K.    Unpublished  curriculum,  Center  on  Teaching  and  Learning,  University  of  Oregon,  Eugene,  OR.  

Doabler,  C.  T.,  Cary,  M.  S.,  Jungjohann,  K.,  Clarke,  B.,  Fien,  H.,  Baker,  C.,  Smolkowski,  K.,  &  Chard,  D.  (2012).  Enhancing  core  mathematics  instruction  for  students  at  risk  for  mathematics  disabilities.  Teaching  Exceptional  Children,  44(4),  48-­‐57.  

Flores,  M.  M.,  Hinton,  V.,  &  Strozier,  S.  (2014).  Teaching  subtraction  and  multiplication  with  regrouping  using  Concrete-­‐Representational-­‐Abstract  sequence  and  the  Strategic  Instruction  Model.  Learning  Disabilities  Research  and  Practice,  29(2),  75-­‐88.  

Fuchs,  L.  S.,  &  Fuchs,  D.  (2008),  Mathematics  disabilities  in  the  primary  grades:  Seven  principles  of  effective  practice.  Retrieved  from  www.TeachingLD.org  

Gagnon,  J.,  &  Maccini,  P.  (2001).  Preparing  students  with  disabilities  for  algebra.  Teaching  Exceptional  Children,  34(1),  10-­‐17.  

Gargiulo,  R.  M.,  &  Metcalf,  D.  (2013).  Teaching  in  today’s  inclusive  classrooms:  A  universal  design  for  learning  approach  (2nd  ed.)  Independence,  KY:  Cengage  Learning.  

Geary,  D.  C.  (2004).  Mathematics  and  learning  disabilities.  Journal  of  Learning  Disabilities,  37,  4-­‐15.  

Jitendra,  A.  K.,  Rodriguez,  M.,  Kanive,  R.,  Huang,  J.,  Church,  C.,  Conrroy,  K.  A.,  &  Zaslofsky,  A.  (2013).  Impact  of  small-­‐group  tutoring  interventions  on  the  mathematical  problem  solving  and  achievement  of  third-­‐grade  students  with  mathematics  difficulties.  Learning  Disability  Quarterly,  36,  21-­‐35.  

Maccini,  P.,  &  Gagnon,  J.  (2005).  Mathematics  strategy  instruction  (SI)  for  middle  school  students  with  learning  disabilities.    The  Access  Center.  Retrieved  from  http://digilib.gmu.edu/jspui/bitstream/1920/284/1/MathSIforMiddleSchoolStudentswithLD.2.pdf  

Mastropieri,  M.  A.,  &  Scruggs,  T.  E.  (2002).  Effective  instruction  for  special  education  (3rd  ed.).  Austin,  TX:  PRO-­‐ED.  

Mazzocco,  M.  (2007).  Defining  and  differentiating  mathematical  learning  disabilities  and  difficulties.  In  D.  Berch  &  M.  Mazzocco  (Eds.),  Why  is  math  so  hard  for  some  children?  The  nature  and  origins  of  mathematics  learning  difficulties  and  disabilities  (pp.  29-­‐47).  Baltimore,  MD:  Paul  H.  Brooks.  

Mercer,  C.  D.,  Mercer,  A.  R.,  &  Pullen,  P.  C.  (2011).  Teaching  students  with  learning  problems  (8th  ed.).  Upper  Saddle  River,  NJ:  Pearson  Education.  

Mercer,  C.  D.,  &  Miller,  S.  P.  (1992).  Multiplication  facts  0  to  81.  Lawrence,  KS:  Edge  Enterprises.  

Mevarech,  Z.  R.,  &  Amrany,  C.  (2008).  Immediate  and  delayed  effects  of  meta-­‐cognitive  instruction  on  regulation  of  cognition  and  mathematics  achievement.  Metacognition  and  Learning,  3(2),  147-­‐157.  

National  Center  for  Education  Evaluation  and  Regional  Assistance.  (2009).  Assisting  students  struggling  with  mathematics:  Response  to  intervention  (RtI)  for  elementary  and  middle  schools  (Practice  Guide  Report  No.  NCEE  2009-­‐4060).  Washington,  DC:  Institute  of  Education  Sciences.  Retrieved  from  http://ies.ed.gov/ncee/wwc/pdf/practice_guides/rti_math_pg_042109.pdf  

 National  Governors  Association  Center  for  Best  Practices,  Council  of  Chief  State  School  Officers.  (2010).  Common  Core  State  Standards  (Mathematics).  Washington,  DC:  National  Association  Center  for  Best  Practices,  Council  of  Chief  State  School  Officers.  Retrieved  from  http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf  

National  Governors  Association.  (2014).  Trends  in  state  implementation  of  the  common  core  state  standards:  Making  the  shift  to  better  tests.  Retrieved  from  http://www.nga.org/files/live/sites/NGA/files/pdf/2014/1404NGACCSSAssessments.pdf  

Owen,  M.  J.  (2003).  It’s  elementary!  275  math  word  problems  book  3.  Toronto,  Canada:  Educator  Publishing  Service.  

Powell,  S.  R.,  Fuchs,  L.  S.,  &  Fuchs,  D.  (2013).  Reaching  the  mountaintop:  Addressing  the  common  core  standards  in  mathematics  for  

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students  with  mathematics  difficulties.  Learning  Disabilities  Research  and  Practice,  28,  38-­‐48.  doi:  10.1111/ldrp.12001  

Sayeski,  K.  L.,  &  Paulsen,  K.  J.  (2010).  Mathematics  reform  curricula  and  special  education:  Identifying  intersections  and  implications  for  

practice.  Intervention  in  School  and  Clinic,  46,  13-­‐21.  

Sliva,  J.  A.  (2004).  Teaching  inclusive  mathematics  to  special  learners,  K-­‐6.  Thousand  Oaks,  CA:  Corwin  Press.  

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